On 24 jul, 17:07, gwh <ghug...@cei.net> wrote:> On Jul 24, 9:36 am, arithmonic <djes...@gmail.com> wrote:>>>> My, my! Leave town for a few days, and look what happened while my> back was turned! I've never been so popular before, and all because I> remarked that an old text showed how to extract cube roots! Well, here> it is-- I'll do the best I can to type it in a form that I hope will> be readable.

YOU GOT A CHEEK, INDEED.YOUR UNETHICAL ATTITUDE ONLY MATCH THAT FROM OTHERS IN THE PAST INTHIS NEWGROUP.EXACTLY THE SAME UNETHICAL ATTITUDE.

Now, I am free to respond to BOTH OF you as you deserve before thesci.math audience because it has been proven that you and your friendGrover Hughes were making just FALSE STATEMENTS.

Grover Hughes negligently wrote:On 16 jul, 18:24, gwh <ghug...@cei.net> wrote:> On Jul 14, 10:30 pm, arithmeticae <djes...@gmail.com> wrote:> > If you really like to analyze the most simple high-order root-solving algorithms then you should take a look at:> >http://mipagina.cantv.net/arithmetic/rmdef.htm> > It is striking to realize that these new extremely simple artihmetical algorithms do not appear in any text on numbers since Babylonian times up to now.>> Maybe not in "any text on numbers", but back in 1945 I purchased a> copy of "Handbook of Engineering Fundamentals", by Eshbach, and the> cube root extraction scheme described there was precisely the same as> the scheme described on one of the links given on the above website.

and his friend also <sttscitr...@tesco.net> negligently wrote:

On 24 jul, 06:44, "sttscitr...@tesco.net" <sttscitr...@tesco.net>wrote:> Your historical claim may well be true, but at> least one poster states he has a reference predating your> claim. It would be interesting if he could post the method> he found in the Handbook

All the two assertions from Grover Hughes and his friend<sttscitr...@tesco.net> has been provento be absolutely FALSE and UNETHICAL STATEMENTS. Their alleguedHurtwitz 's method (which in fact his originator was Achimedes orWallis if you prefer) and Eshbach's method are not by far the samethat the ones shown in my pages.

Notwithstanding, forget it, I do not care of such unethical attitudeas well as i did not care for the shameful attitude from others in thepast, the main point that I really care is the following:

I face and mantain my assertions: "THE EXTREMELY SIMPLE HIGH-ORDERMETHODS SHOWN IN MY WEBPAGES --BASED ON THE RATIONAL MEAN-- DO NOTAPPEAR IN NEITHER ANY CHINESE, NOR ARAB, NOR INDIAN, NOR WESTERN BOOK,since ancient Babylonian times UP TO NOW!!! AND YOU WILL REALIZE THATNO MATHEMATICIAN nor any math-historian will be able to deny such acrude fact.And this is a real shame mainly for all of us who have read some aboutthe very long history of root solving.

What do think it would had happened if, for instance, Plat?n,Nichomacus, Wallis, etc. would had found such high-order arithmeticalmethods in such a trivial-arithmetical way?Consider that all those mathematicians from past times (includingNewton, Halley,etc.) certainly had the elementary tools to do that, however, from theevidence at hand THEY DIDN'T, and this is something really strikingfor anyone who have ever read a book on the history of mathematics.

If these methods --based on the RATIONAL MEAN-- would had beendiscovered in past times then it is for sure that your math-teacherswould had taught them to you at school. that's simple.

That is what really matters here, because this leads to think how manyother thing are we missing.I am sure there another very different mathematics from that we haveinherited and all these new simple methods are a clear evidence ofthat.There is certainly a missing mathematics and young minds certainlyhave the most simple tools to find it. we have to break the chainsfrom past times.

On 24 jul, 12:41, "sttscitr...@tesco.net" <sttscitr...@tesco.net>wrote:> On 24 Jul, 16:12, arithmonic <djes...@gmail.com> wrote:>> > *************> > But your statement about that I claimed to have solved the cube Pell's> > equation is another absolute FALSE STATEMENT from yours.>> No, you have obvuiosly forgotten, my comments on> your insane rantings some years ago.>> You should be able to find them by searching for> Morin, Davidson, Pell.>> You were also claiming that your methods could solve> the standard Pell equation. Claims which also> turned out to be wrong. You have never> admiited that you were wrong. But that would be too much> to expect.

Yes, in this newsgroup you and some others guys in the past tried todo exactly thesame unethical acts than you and your friend Grover Hughes have triedthis time.You got a cheek, indeed.You and all your friends should cogitate on your unethical attitude.

In past times, You insisted to say that the methods shown in mywebpages donot yield best approximations and I told you and again I tell you thistime that such methods certainly produce best approximations. The factthat some of those methods based on the Rational Mean could notproduce ALL the best approximations is another problem which is thesame problemwith Newton's, Halley's, etc. when computing some particular roots.

I challenge you to show a posting from mine saying exactly what youare attributing to me,that is: "I can solve the cube version of Pell equation"That is another FALSE STATEMENT FROM YOURS, as FALSE as all the otherstatements that youand your friend Grover Hughes pretended to state in order to preventpeople from reading my book and webpages. But you have failed again inthe same way that in past times you and others did.

You, your friend Grover Hughes and some others from past times havehad the same unethical attitude,many of you use to form kind of packs and make all kind of FALSEstatements causing confusion and preventing people from reading one'swork. That's an unethical attitude.

But, you know? I don't care and I have never cared of such packs andunethical attitude, because the methods shown in my webpages easilydemolish all such unethical attempts, and such trivial high-ordermethods will remain there even after I have died out.

What I have always said is that my methods embrace Newton's,Bernoulli's, Halley's, Househloder'sand many other NEW iterating functions for solving roots. My method isnot just one algorithm buta new general and very simple concept involving so many high-ordermethods.The point these methods are based on the most simple arithmetic andthat is really striking mainlywhen considering the very long story on root-solving.

The methods shown in my pages :http://mipagina.cantv.net/arithmetic/rmdef.htmDO CERTAINLY YIELD BEST APPROXIMATIONS, of course they CERTAINLY DO,and I AM SURE that the NEW ARITHMONIC MEAN is the best tool to workthe cube version of PELL'S EQUATION, and that is all what I have eversaid.IF YOU LIKE TO ENJOY BEST APPROXIMATIONS, THEN LOOK AT THE ARITHMONICMEAN PROCESSES SHOWN IN MY WEBPAGES. That hurt yours and some othersfeelings (mainly math-historians) but that's not my fault,ask mathematicians from past times why they didn't developed suchTRIVIAL HIGH-ORDER ARITHMETICAL NON-TRIAL-&-NON-ERROR ALGORITHMS.

I have no intentions of sending these NEW methods to any peer-reviewjournal, I don't need to give detailed explanations on why, I think myreasons are very fairly clear.I think this is matter of ETHICS, MORAL AND UN-BIASING MATHEMATICS.

If a math-historian take a look through all those new simplearithmetical methods --based on the rational mean-- the suchmathematician must have the MORAL OBLIGATION to make comments andinclude some analysis on them in his books, papers, etc. THAT JUST AMATTER OF MORAL AND ETHICS, MAINLY WHEN CONSIDERING THE VERY LONGSTORY ON ROOT-SOLVING.